If a training data has additional information, such as labels, we can train a neural network jointly with supervised training for specific related tasks such as conditional generation, where we want samples that correspond to a desired class. We can condition the latent variables to have different distributions from different classes. The output of the network is trained from the Gaussian distribution \(\textbf {z} \sim Q(z_i,c_i),\)  with \(c_i\)  being a one-hot vector containing the class information. Similar to the work done in Ref. [1]}, we couple a linear classification layer on top of the network, parallel to the mean and variance layers. Since the class layer is linear, at inference time we can choose a greater value for the one-hot vector, which puts emphasis on the chosen class.
